You could try the Emirates Flying School (Emirates Aeroclub) based beside terminal 2 Dubai International Airport , ph 04 2995155 however there prices are high and I found there attitude was somewhat non productive to a safe flying environment, but you can't take everthing on first impressions. If you just want a quick scenic and to say you have flown in the mid east this could be the place you are looking for as it has location, I checked for you and you are looking at 600.00 dhms per hour for a PA 28-181 or 550.00 dhms for a PA 28-161, (at that price you would expect shares in the aircraft or at least jet time ) . There is another aeroclub in RAK but the location and phone number prove hard to come by. Maybe someone alse can help out there.
Hope you have a good one